The LHC collider and its detectors have been a generational effort to design, construct, and commission, with the primary mission to understand the nature of electroweak symmetry-breaking and the origin of rest-mass for fundamental particles. The discovery of the Higgs boson in 2012 marked a major achievement for particle physics, but this discovery has brought a number of long-standing puzzles into sharper focus. I will discuss several of these questions and how the University of Minnesota CMS group is addressing them. These questions include neutrino mass and left-right symmetry in particle interactions, the internal consistency of the Standard Model, and the nature of cosmological dark matter.